The Foundations of Chemistry

Ammonium ions from NH 4 Cl react to some extent with OHto form nonionized NH 3
and H 2 O molecules. This reaction removes OHfrom the system, so it causes more H 2 O
to ionize to produce an excess of H 3 O
. The net result of the preceding equations can
be written as a single equation with its equilibrium constant expression.

NH 4 

H 2 O 34 NH 3 
H 3 O
 Ka

The expression KwKaKbis valid for anyconjugate acid–base pair in aqueous solution.
We use it for the NH 4
/NH 3 pair.

Ka (NH 4 
)5.6 10 ^10 

The fact that Kafor the ammonium ion, NH 4
, is the same as Kbfor the acetate ion
should not be surprising. Recall that the ionization constants for CH 3 COOH and aqueous
NH 3 are equal (by coincidence). Thus, we expect CH 3 COOto hydrolyze to the same
extent as NH 4
does.

EXAMPLE 18-20 pH of a Soluble Salt

Calculate the pH of a 0.20 Msolution of ammonium nitrate, NH 4 NO 3. Kafor NH 4

5.6 10 ^10.

Plan

We recognize that NH 4 NO 3 is the salt of a weak base, NH 3 , and a strong acid, HNO 3 , and
that the cations of such salts hydrolyze to give acidic solutions. We proceed as we did in Example
18-19.

Solution

The cation of the weak base reacts with H 2 O. Let xmol/L of NH 4
that hydrolyzes. Then
x[NH 3 ][H 3 O
].

NH 4 
 
H 2 O 34 NH 3 
H 3 O


initial 0.20 M 0 M 
 0 M

change due to rxn x M 
x M 
x M

at equil (0.20x) Mx Mx M

Substituting into the Kaexpression gives

Ka5.6 10 ^10

Making the usual simplifying assumption gives x1.1 10 ^5 M[H 3 O
] and pH4.96.
The 0.20 MNH 4 NO 3 solution is distinctly acidic.

You should now work Exercise 90.

(x)(x)



(0.20x)

[NH 3 ][H 3 O
]



[NH 4 
]

[NH 3 ][H 3 O
]



[NH 4 
]

1.0 10 ^14



1.8 10 ^5

Kw



Kb (NH 3 )

[NH 3 ][H 3 O
]



[NH 4 
]

NH 4 Cl(solid) NH 4 
 
 Cl

NH 3 
 H 2 O

OH 
 H 3 O

(result is excess H 3 O
)

H 2 O

100%

H 2 O 
 H 2 O

Equilibrium is shifted

Similar equations can be written for

cations derived from other weak bases

such as CH 3 NH 3 
and (CH 3 ) 2 NH 2 
.

If you wish to derive KaKw/Kbfor

this case, multiply the Kaexpression by

[OH]/[OH] and simplify.

Ammonium nitrate is widely used as a

fertilizer because of its high nitrogen

content. It contributes to soil acidity.

18-9 Salts of Weak Bases and Strong Acids 781

The pH of 0.20 MNH 4 NO 3

solution is 4.96.

Salt of

weak base/strong acid

Acidic

aqueous solution

m8888